Cycles vs internal vs game engine
Besides what is stated in the linked question about the differences between Blender Internal and Cycles what I can add is the following

Historically speaking Cycles is a relatively new addition to Blender. It is a completely external and standalone rendering Engine that interacts with Blender through a built in plugin and python API.
Cycles can even be used with other applications as a standalone rendering solution

Blender Internal on the other hand is integral part of Blender. It is very old, as old as Blender itself, it has been deeply improved throughout the years, but is still deeply integrated and a fundamental part of Blender, without which Blender would not work.

Its material system is also deeply tied to the OpenGL viewport preview system, that is why it's material settings and node setup are very similar to the Game Engine which uses the same OpenGL render engine.

It's also why it has a better more complete material preview system in the viewport. Where Cycles material preview is very basic and limited to image based textures without any kind of shading.

That is bound to change in the future though, Blender 2.78 already has a better preview for procedural textures, and a substantial upgrade is being made for the Blender 2.8 project.

First decoupling and removing dependencies of the Internal Render, modernizing the OpenGL real time preview, and then creating a modern substitute of Blender Internal

I know of no plugins that work with Blender rendering engines, but you can use the built in Compositor for post processing, or any external compositing software that you desire.